Related papers: Equations in a free group. Elementary theory
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We prove that the isomorphism problem for finitely generated fully residually free groups is decidable. We also show that each finitely generated fully residually free group G has a decomposition that is invariant under automorphisms of G,…
We consider an homogeneous action of a finite group on a free linear category over a field in order to prove that the subcategory of invariants is still free. Moreover we show that the representation type is preserved when considering…
Takahasi's theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of periodic points are finitely generated and periodic orbits…
We prove a ratio ergodic theorem for amenable equivalence relations satisfying a strong form of the Besicovich covering property. We then use this result to study general non-singular actions of non-abelian free groups and establish a ratio…
We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete
Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as epigroup. We prove the following theorem announced by Zhil'tsov in 2000: the equational theory of the…
We prove that for any automorphism $\alpha$ of a free group F of finite rank, one can efficiently compute a basis of the fixed point subgroup Fix(\alpha).
We prove the following propositions. Theorem 1: Let $M$ be a subfield of a fixed algebraic closure $\tilde \Q$ of $\Q$ whose existential elementary theory is decidable (resp. primitively decidable). Then, M is conjugate to a recursive…
We prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.
We construct easy embeddings of relatively free groups (say the free Burnside group, the free solvable group) into finitely presented groups. We introduce a concept of verbal isoperimetric function of a group variety. We prove that if the…
Free groups have many applications in Algebraic Topology. In this paper I specifically study the finitely generated free groups by using the covering spaces and fundamental groups. By the Van Kampen's theorem, we have a famous fact that the…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
We prove various finite de Finetti theorems for non-commutative distributions which are invariant under the free easy quantum group actions. This complements the free de Finetti theorems by Banica, Curran and Speicher, which mostly focus on…
We prove an interpolation theorem for bounded free holomorphic functions.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We prove that the Diophantine problem for orientable quadratic equations in free metabelian groups is decidable and furthermore, NP-complete. In the case when the number of variables in the equation is bounded, the problem is decidable in…
In this paper we find a characterization for groups elementarily equivalent to a free nilpotent group $G$ of class 2 and arbitrary finite rank.
We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…